Design and Analysis of Gallium Arsenide-Based Nanowire Using Coupled Non-Equilibrium Green Function for RF Hybrid Applications

This research work uses sp3d5s* tight-binding models to design and analyze the structural properties of group IV and III-V oriented, rectangular Silicon (Si) and Gallium Arsenide (GaAs) Nanowires (NWs). The electrical characteristics of the NWs, which are shielded with Lanthanum Oxide (La2O3) material and the orientation with z [001] using the Non-Equilibrium Green Function (NEGF) method, have been analyzed. The electrical characteristics and the parameters for the multi-gate nanowires have been realized. A nanowire comprises a heavily doped n+ donor source and drains doping and n-donor doping at the channel. The specified nanowire has a gate length and channel length of 15 nm each, a source-drain device length LSD = 35 nm, with La2O3 as 1 nm (gate dielectric oxide) each on the top and bottom of the core material (Si/GaAs). The Gate-All-Around (GAA) Si NW is superior with a high (ION/IOFF ratio) of 1.06 × 109, and a low leakage current, or OFF current (IOFF), of 3.84 × 10−14 A. The measured values of the mid-channel conduction band energy (Ec) and charge carrier density (ρ) at VG = VD = 0.5 V are −0.309 eV and 6.24 × 1023 C/cm3, respectively. The nanowires with hydrostatic strain have been determined by electrostatic integrity and increased mobility, making them a leading solution for upcoming technological nodes. The transverse dimensions of the rectangular nanowires with similar energy levels are realized and comparisons between Si and GaAs NWs have been performed.


Introduction
Over the last two decades in the semiconductor industry, the advanced structure of Metal Oxide Semiconductor Field Effect Transistors (MOSFETs), from planar to multi-gate design, has been proposed to achieve great electrostatic control over the channel. Various multi-gate structural designs named Double gate, Tri-gate, Pi, Omega, Top on-one side, and Gate-all-around (GAA) devices with nanotechnology approaches have been used for forthcoming applications. The GAA device architecture has high resistance properties. It exhibits static control on the gate over the conduction of the channel, which plays a major role in avoiding short-channel effects [1,2]. Natori et al. [3] have proposed GAA NW to resist (SCEs) by improving gate length and channel length scaling (L G < 5 nm and L ch < 15 nm). The primary benefit of GAA devices is that they have a higher I ON /I OFF ratio [4]. The reduction in OFF current (I OFF ) produces a high (I ON /I OFF ) ratio. Batakala et al. [5] have demonstrated the comparison between Si and GaAs GAA MOSFETs. The gain and currentdriving capacity of the GaAs material were efficient and, thus, based on this channel material, was selected following the application field. The reduction in leakage current had been achieved by considering major features, such as smaller threshold voltage (V th~0 .3 V), 3 of 20 depends on the nanowire's width. The symmetrical character of the d 001 orbital has the same width dependence configuration of p 001 , but the magnitude of orbital d 001 was found to be lesser, about nanowire based from p 001 . This work concentrates on designing a novel nanowire-based on GaAs material to use in RF hybrid applications. To improve the I ON and I OFF ratio, various methodologies have been utilized. The usage of high-Nanomaterials 2023, 13, x FOR PEER REVIEW 3 of 21 Morioka et al. [26] have presented the electronic band structures of rectangular Si NWs using sp 3 d 5 s* tight-binding models. This method considers one excited s* orbital, p orbitals {px, py, and pz}, and d orbitals {dyz, dzx, dxy, d3z 2 -r 2 , and dx 2 -y 2 }. The x, y, and z coordinate axes are set at [100], [010], and [001], respectively. The part of each atomic orbital typically depends on the nanowire's width. The symmetrical character of the d001 orbital has the same width dependence configuration of p001, but the magnitude of orbital d001 was found to be lesser, about nanowire based from p001. This work concentrates on designing a novel nanowire-based on GaAs material to use in RF hybrid applications. To improve the ION and IOFF ratio, various methodologies have been utilized. The usage of high ƙ dielectric material, such as La2O3, has shown various enhancements to create an optimal design to be used in RF application setups. This paper has been organized as follows. The basics of NEGF modeling have been discussed in Section 2. The proposed nanowire structure with six variants has been discussed in Section 3. The mathematical modeling of lanthanum oxide with the self-consistent methodology and the division of the 3D problem into 1D transport and 2D Schrodinger equations were investigated in Section 4. Section 5 discusses the lt and analysis of the work. Finally, Section 6 concludes the work and recommends the future aspects.

Basics of NEGF Modeling
The electronic properties of hydrogen-passivated compound semiconductor nanowires grown in different crystallographic orientations, specifically the band structures, band gaps, and effective electron masses, were discussed previously [27][28][29][30]. Horiguchi et al. [31] have discussed the Silicon nanowire bandgap dependency on the wire width using effective mass theory calculations and using the boundary conditions envelope between wire confinement potential and the barrier height confinement potential's finiteness. Several authors have presented nanoscale modeling using green's function, quantum transport modeling, density matrix calculation, and analyzing electronic devices in equilibrium conditions [32][33][34][35].
Seone et al. [36] have proposed the Gate-All-Around (GAA) Si nanowire MOSFET and the impact of current variability on the channel's surface roughness was analyzed using 3-D real-space non-equilibrium Green's function. Mazumder et al. [37] have proposed GAA GaAs TFET, which works under the tunneling phenomenon. The maximum ION/IOFF ratio of TFET is achieved by adjusting the few electric gate insulator and GAA TFET channel architecture, which were been investigated to provide the best band-toband tunneling and potential amplification. Montazeri et al. [38] have demonstrated the band structure for III-V compound semiconductor nanowires using k.p theory calculations. The calculation of the strain is used to determine the particular nanowire structure, and it had been employed using the elastic theory. The resulting calculated strain was called hydrostatic strain, which depends on the proportions of structural dimensions and is independent of the total size. Ren et al. [39] have modeled nanoscale MOSFETs and estimated the scattering and backscattering coefficients using the scattering theory. The critical length and carrier velocity at the source's end and the channel's start were identified using transport models. The ballistic, dual-gate nano transistors used for digital applications with a proper choice of the gate oxide thickness and scaling limit down to 10 nm were discussed [40,41]. Several studies have incorporated the operation of the nanowire in a ballistic regime using analytic models [42][43][44][45] and numerical simulations [46,47]. In the simulation study, the density of states, the electron density, and the conduction band energy (Ec) variations along the position of the channel were investigated [48].

Design of Proposed Novel GaAs Nanowire
The generic structure of the proposed nanowire has been designed with a rectangular cross-section with dimensions of 35 nm × 4.5 nm. The source and drain of the Si and GaAsbased nanowire material have a continuous n + donor impurity concentration of (2 × 10 20 dielectric material, such as La 2 O 3 , has shown various enhancements to create an optimal design to be used in RF application setups. This paper has been organized as follows. The basics of NEGF modeling have been discussed in Section 2. The proposed nanowire structure with six variants has been discussed in Section 3. The mathematical modeling of lanthanum oxide with the self-consistent methodology and the division of the 3D problem into 1D transport and 2D Schrodinger equations were investigated in Section 4. Section 5 discusses the lt and analysis of the work. Finally, Section 6 concludes the work and recommends the future aspects.

Basics of NEGF Modeling
The electronic properties of hydrogen-passivated compound semiconductor nanowires grown in different crystallographic orientations, specifically the band structures, band gaps, and effective electron masses, were discussed previously [27][28][29][30]. Horiguchi et al. [31] have discussed the Silicon nanowire bandgap dependency on the wire width using effective mass theory calculations and using the boundary conditions envelope between wire confinement potential and the barrier height confinement potential's finiteness. Several authors have presented nanoscale modeling using green's function, quantum transport modeling, density matrix calculation, and analyzing electronic devices in equilibrium conditions [32][33][34][35].
Seone et al. [36] have proposed the Gate-All-Around (GAA) Si nanowire MOSFET and the impact of current variability on the channel's surface roughness was analyzed using 3-D real-space non-equilibrium Green's function. Mazumder et al. [37] have proposed GAA GaAs TFET, which works under the tunneling phenomenon. The maximum I ON /I OFF ratio of TFET is achieved by adjusting the few electric gate insulator and GAA TFET channel architecture, which were been investigated to provide the best band-to-band tunneling and potential amplification. Montazeri et al. [38] have demonstrated the band structure for III-V compound semiconductor nanowires using k.p theory calculations. The calculation of the strain is used to determine the particular nanowire structure, and it had been employed using the elastic theory. The resulting calculated strain was called hydrostatic strain, which depends on the proportions of structural dimensions and is independent of the total size. Ren et al. [39] have modeled nanoscale MOSFETs and estimated the scattering and backscattering coefficients using the scattering theory. The critical length and carrier velocity at the source's end and the channel's start were identified using transport models. The ballistic, dual-gate nano transistors used for digital applications with a proper choice of the gate oxide thickness and scaling limit down to 10 nm were discussed [40,41]. Several studies have incorporated the operation of the nanowire in a ballistic regime using analytic models [42][43][44][45] and numerical simulations [46,47]. In the simulation study, the density of states, the electron density, and the conduction band energy (E c ) variations along the position of the channel were investigated [48].

Design of Proposed Novel GaAs Nanowire
The generic structure of the proposed nanowire has been designed with a rectangular cross-section with dimensions of 35 nm × 4.5 nm. The source and drain of the Si and GaAs-based nanowire material have a continuous n + donor impurity concentration of (2 × 10 20 cm −3 ) and n donor doping of (1 × 10 20 cm −3 ) at the channel. The channel direction in this situation is longitudinal to the <001> z-axis, 'x' determines the channel width, and 'y' determines the current flow into the nanowires, as shown in Figure 1a. The electron movement in the longitudinal z direction is based on Kinetic Energy (E z ) and is called Transmission Probability T (E z ). The proposed nanowire dimensions are listed in Table 1.  The Landauer formula, as in reference [3], yields the following description of the drain current:  The Landauer formula, as in reference [3], yields the following description of the drain current: where 'n' is the quantum number that matches the confinement in the wire cross-section; E FL , and E FR (=E FL − eV DS ), where E FL and E FR are the fermi energy levels at the source and drain. Equation (2) is the Fermi-Dirac Distribution. E nv , n in Equation (3) fits into the particular valley n v , where n v = 1, 2, 3, represents the energy confinement level at the top barrier on the channel as (E top = E FL + k B T). In Figure 1b, the potential energy distribution is along the z-axis, where the maximum energy at the uppermost oxide interface from the channel is represented as E max . The Landauer equation can be simplified as follows: Equation (4) determines the current I DS where confinement energy levels at the oxide interface top barrier z max exist. Multiple gates or very thin film structures were necessary to control SCEs in III-V technologies, as suggested previously [3]. There are six variants shown in Figure 2. Each variant differs in the number of gates and their arrangement with natural length, as shown in Table 2. particular valley nv, where nv = 1, 2, 3, represents the energy confinement level at the top barrier on the channel as (Etop =EFL + kBT). In Figure 1b, the potential energy distribution is along the z-axis, where the maximum energy at the uppermost oxide interface from the channel is represented as Emax. The Landauer equation can be simplified as follows: , , , Equation (4) determines the current IDS where confinement energy levels at the oxide interface top barrier zmax exist. Multiple gates or very thin film structures were necessary to control SCEs in III-V technologies, as suggested previously [3]. There are six variants shown in Figure 2. Each variant differs in the number of gates and their arrangement with natural length, as shown in Table 2. The natural length λn can be calculated by: where 'ñ' is referred to as the effective number of gates. The idea was to design devices with both doped and undoped channels that use mid-gap gate material and yields the highest gate efficiencies for sub-10 nm technology [27,28]. The device's short-channel behavior has been enhanced by raising the equivalent gate number 'ñ' and by maintaining the size of the gate length (approximately) five to ten times greater than that of the natural length λn. Scaling is possible with GAA devices because they are built with the gate in contact with the channel on all sides. The main benefit of GAA devices is that they have a higher ION/IOFF ratio. Owing to the asymmetric characteristics of the electrostatic control, the tri-  The natural length λ n can be calculated by: where 'ñ' is referred to as the effective number of gates. The idea was to design devices with both doped and undoped channels that use mid-gap gate material and yields the highest gate efficiencies for sub-10 nm technology [27,28]. The device's short-channel behavior has been enhanced by raising the equivalent gate number 'ñ' and by maintaining the size of the gate length (approximately) five to ten times greater than that of the natural length λ n . Scaling is possible with GAA devices because they are built with the gate in contact with the channel on all sides. The main benefit of GAA devices is that they have a higher I ON /I OFF ratio. Owing to the asymmetric characteristics of the electrostatic control, the tri-gate arrangement results in a lower gate-controlled charge and is 25% smaller when compared to the GAA SiNW for the specific W/H ratio because there are more channel sides placed towards the gate contact.
When the gate voltage V G = 0 V, the potential in three-dimensional form has been distributed out over the length of the NW, as shown in Figure 3, which is represented in the order of Double gate, GAA, Omega, Pi, Top, and Tri-gate respectively. Three different effective masses (m l , m t , m t ), (m t , m l , m t ), and (m t , m t , m l ) have been considered for the x, y, and z directions. The (m l ) and (m t ) are the longitudinal and transverse effective masses whose value is equal to 0.98 m 0 and 0.19 m 0. The mass (m 0 ) is called free electron mass.

Mathematical Modeling of the Nanowire with La2O3
The proposed multi-gate device is a 3-D-dimensional nanowire with a source and drain doping concentration of 2 × 10 20 cm 3 . The source and drain are made of silicon or gallium arsenide that has been highly doped with n + atoms. The device's effective mass Hamiltonian has been denoted by the notation:

Mathematical Modeling of the Nanowire with La 2 O 3
The proposed multi-gate device is a 3-D-dimensional nanowire with a source and drain doping concentration of 2 × 10 20 cm 3 . The source and drain are made of silicon or gallium arsenide that has been highly doped with n + atoms. The device's effective mass Hamiltonian has been denoted by the notation: where the conduction band edge profile is represented by V (x, y, z) [26], and m * x , m * y , and m * z are the effective masses: where E C1/2 (x, y) is the band gap of the nanowire core material (Si/GaAs), the point (x, y) links to the dioxide region, and (x, y, and z) corresponds to space potential. Due to the movement of electrons in the z-direction, the effective core mass in the transport direction is m* z , and the effective oxide masses are represented by m* x = m* x (x,y) and m* y = m* y (x,y), respectively. The wavefunction of the three-dimensional Hamiltonian (x, y, and z) in the longitudinal z direction is given as: The bth mode eigen function ψ b (x, y; z) represented in two-dimensional (2D) Schro dinger equation is given as: where Under boundary conditions, the wave functions at the margins of the two-dimensional (2D) cross-section plane is known as uncoupled mode space method, which eliminates the coupling among several modes (or sub-bands), and ϕ b (z) satisfies as follows: The Schrodinger Equation (13) with open boundary conditions describes the 1-D transport problem, and further, the NEGF technique [31] has been used to solve it. The primary notation for the sub-band b using 1-D Green's function (G b ) is as follows: where Σ S,b and Σ D,b are the S/D self-energies of sub-band b, respectively. The 1D charge density n k 1D (z) in the bth sub-band is then obtained via: where ∆ x is the lattice spacing, and Γ S,b and Γ D,b are defined by: The Fermi Distribution functions and the Fermi Energies at the source and drain are given as follows: The 3-D quantum charge density has been employed in Poisson's equation after one-dimensional (1D) charge densities of each sub-band are resolve as follows: Equation (21) determines the potential and doping profile (N D ) of (x, y, and z). The current in Equation (22) is calculated using the Landauer-Buttiker formula, once selfconsistency and charge distributions are attained: where the Transmission Probability T b (E) for sub-band 'b' is given by:

Numerical Approaches
The two-dimensional (2-D) Schrodinger equations and the 1-D NEGF equation numerical solutions have been presented. The mass discontinuity across the lanthanum oxide (La 2 O 3 ) contact has been included in the 2-D Schrodinger equation using the following k-space approach.

K-Space Solutions of Two-Dimensional Schrodinger Equations
Let's first rewrite Equation (25) as follows: where A k 's are expansion coefficients and |K is a basic set. The eigenvalue problem is solved by substituting Equation (24) in Equation (10) and multiplying L\ by the equation sides: where H LK 2D A K = L\H 2D |K . In the standard k-space solution [19]: Here, L x and L y are the cross-side section's lengths in the x and y directions, respectively.
The corresponding grid numbers in the x and y directions are N x and N y . It must be noted that the K index is derived with the indices i and j by the formula K = (N x (i − 1) + j) in Equation (26).
A rectangular cross-section with core/oxide interfaces at (x 1 and x 2 ) and (y 1 and y 2 ), respectively (see Figure 4). Equation (29) defines the effective asymmetrical masses at the core/oxide interfaces for the Hamiltonian using H LK 2D and it is given as follows: where where m * core,x and m * core,y are the effective core masses in the x and y directions. The u and v are the indices that are mapped with L in a parallel fashion to the index K, respectively.
where * , For a good approximation, it is written as follows: The oxide region on either side of the core has been considered as (y1 < y < y2) and the amplitude in the top and bottom of the oxide regions are considered as (y < y1 and y > y2), respectively. The band gap of the oxide materials is substantially wider than that of the core material. Equations (36) and (37)

Product Space Solutions of 2-D Schrodinger Equations
From Figure 4, the rectangular cross-section with effective mass is represented as follows: where For a good approximation, it is written as follows: The oxide region on either side of the core has been considered as (y 1 < y < y 2 ) and the amplitude in the top and bottom of the oxide regions are considered as (y < y 1 and y > y 2 ), respectively. The band gap of the oxide materials is substantially wider than that of the core material. Equations (36) and (37) define the effective masses in the y direction: where m * y (y) = m * core,x if y 1 ≤ y ≤ y 2 m * ox if y < y 1 or y > y 2 (37) The adjacent side of the oxide effective mass regions is inappropriate for the above reasons. Therefore, it is written as under good approximation: The following equation is the product-space solution: Equation (40) determines the 1D Schrodinger equation in the x direction, where χ i is the ith Eigen function: where ζ j (y) is the jth eigen function and V(x,y) is the confinement potential for the following 1-D Schrodinger equation in the y-direction: where Substituting Equation (39) in Equation (38) and obtaining Equations (40)- (43).
By multiplying L\ in Equation (44), we obtain: where After resolving the Schrodinger equations, the eigenvalue problem and the productspace solution have been found. Equations (40) and (42) illustrate one dimensional (1-D) version of the k-space solution approach, which was introduced in the previous section and has been employed in the modeling.

Analysis of the GaAs-Based Nanowire
There are six possible structures that have been considered in the simulated NWs. Two distinct materials (Si and GaAs), the Double Gate (DG), Gate-All-Around (GAA), Omega, Pi, Top, and Tri-gate variants have been discussed. Figure 2 depicts the rectangular structure with the physical dimensions of all six variants. The crystallographic orientation z <001> direction has coincided with the channel transport direction. The design parameters of the nanowire, listed in Table 1, have been considered for modeling. The conduction band margins of the NWs for different dielectrics had been addressed previously [49].
Higher gate dielectric constant materials have lower conduction band edges. The SiO 2 has a greater conduction band edge than La 2 O 3 when used as a gate dielectric oxide. Thus, lanthanum oxide (La 2 O 3 ) has been chosen as a better choice for a gate dielectric oxide and it is one of the best reasons to provide conduction at lower energies. The Si and GaAs rectangular nanowire simulations have been designed with the same wire length (L wire = 35 nm). Figure 5 shows the comparison between the first and last state energy. The first and sixteenth energy levels of conduction band electrons in a rectangular wire differ by 22% at the left contact of the fermi level E FL = −5 eV. lar structure with the physical dimensions of all six variants. The crystallograph tation z <001> direction has coincided with the channel transport direction. The parameters of the nanowire, listed in Table 1, have been considered for model conduction band margins of the NWs for different dielectrics had been addresse ously [49]. Higher gate dielectric constant materials have lower conduction ban The SiO2 has a greater conduction band edge than La2O3 when used as a gate d oxide. Thus, lanthanum oxide (La2O3) has been chosen as a better choice for a gat tric oxide and it is one of the best reasons to provide conduction at lower energie and GaAs rectangular nanowire simulations have been designed with the sam length (Lwire = 35 nm). Figure 5 shows the comparison between the first and last ergy. The first and sixteenth energy levels of conduction band electrons in a rect wire differ by 22% at the left contact of the fermi level EFL = −5 eV. Based on the full-band model (sp 3 d 5 s*) model, Figure 6 illustrates transmission coefficients for the 2.5 nm wire in the conduction band. The conduction band reaches high transmission when the thickness of the wire get decreases, as shown previously [50,51].
The ballistic current has been calculated by a comparison of the transmission and energy. The transmission steps depend on the channel and have high transmission regions at an energy E = 2.6 eV. The energy differences are nearly parallel; the higher transmission obtained for both Si and GaAs nanowires are 2.8892 eV and 3.5768 at 2.6 eV. Hence, the GaAs is 1.23 times greater than Si NW. Maximum transmission can be achieved with an increase in wire dimension. Higher transmission had been achieved using different orientations with an increase in gate bias, as shown previously [20]. The transmission spectrum has been fixed with zero gate bias (V G ) and a drain voltage (V D ) of 0.6 V. When the gate voltage increases, higher transmission is achieved due to the lowering of the barrier. To normalize the current density in ballistic conditions, the effective width (W eff ) is assumed to be four times the channel width (W ch ), as shown previously [11,52]. The ballistic current has been calculated by a comparison of the tran energy. The transmission steps depend on the channel and have high transmi at an energy E = 2.6 eV. The energy differences are nearly parallel; the higher obtained for both Si and GaAs nanowires are 2.8892 eV and 3.5768 at 2.6 eV GaAs is 1.23 times greater than Si NW. Maximum transmission can be achi increase in wire dimension. Higher transmission had been achieved using di tations with an increase in gate bias, as shown previously [20]. The transmiss has been fixed with zero gate bias (VG) and a drain voltage (VD) of 0.6 V. W voltage increases, higher transmission is achieved due to the lowering of th normalize the current density in ballistic conditions, the effective width (We to be four times the channel width (Wch), as shown previously [11,52]. Figure 7 shows the normalized current density spectra (iz/iz, avg) calcu (fL − fR)), where T is the transmission and (fL − fR) are the left and right fermi l The normalized current density distribution is uniform in the GaAs NW, formity occurs when the Wagner number (Wa > 5), as shown previously [53  Figure 7 shows the normalized current density spectra (i z /i z , avg) calculated by (T × (f L − f R )), where T is the transmission and (f L − f R ) are the left and right fermi level contacts. The normalized current density distribution is uniform in the GaAs NW, and this uniformity occurs when the Wagner number (Wa > 5), as shown previously [53]. The one-dimensional electron density (N1D) along the channel has been plotted against Si and GaAs NW. The comparison has been noticed specifically at the midchannel 'z'. The NEGF calculations are made to compute electron density and the electrostatic potential at the interface. At zero gate bias, there is no creation of a potential barrier and electrons to penetrate the channel. The electron density (N1D ~ 1 × 10 20 ) cm −3 has been ob- The one-dimensional electron density (N 1D ) along the channel has been plotted against Si and GaAs NW. The comparison has been noticed specifically at the midchannel 'z'. The NEGF calculations are made to compute electron density and the electrostatic potential at the interface. At zero gate bias, there is no creation of a potential barrier and electrons to penetrate the channel. The electron density (N 1D~1 × 10 20 ) cm −3 has been obtained in the OFF state when V G = 0 V at the source and decreases more at the midchannel. The electron density increases at the midchannel due to three reasons: (a) Surface Roughness, (b) Higher Gate bias voltage (V G > 0.3 V), or (c) when channel doping is greater than source-drain doping. Here, the middle of the channel has a low electron concentration, which maintains a higher concentration at the drain. The electron densities are uniform throughout the height of the channel, and the GaAs have attained a higher electron concentration at the midchannel than Si NW, as shown in Figure 8. The one-dimensional electron density (N1D) along the channe against Si and GaAs NW. The comparison has been noticed specificall 'z'. The NEGF calculations are made to compute electron density and tential at the interface. At zero gate bias, there is no creation of a p electrons to penetrate the channel. The electron density (N1D ~ 1 × 10 2 tained in the OFF state when VG = 0 V at the source and decreases mor The electron density increases at the midchannel due to three reasons ness, (b) Higher Gate bias voltage (VG > 0.3 V), or (c) when channel do source-drain doping. Here, the middle of the channel has a low elec which maintains a higher concentration at the drain. The electron de throughout the height of the channel, and the GaAs have attained a h centration at the midchannel than Si NW, as shown in Figure 8.  The conduction band energy depends upon the function of both y and z, which is a function of width and length, whereas the sub-band energy minima depends on length [33]. Using the relationship with the carrier velocity, it is concluded that the frequency of electron transmission and channel length are inversely proportional with each other. Thus, the saturation current (I ON ) increases when the channel length gets reduced. The carriers can travel more easily through shorter gate lengths and channel lengths in comparison to a longer channel, as shown previously [45]. The conduction band edge profiles for the GAA variant by fixing V D = 0.5 V and V G have been varied between 0 and 1, as shown in Figure 9. The device gets off at low gate voltages. When gate voltage increases, the potential barrier gets lower, and the energy attained by the electrons will move faster from source to drain and gets lowered with an increase in drain bias.
The conduction band energy decreases at the midchannel when gate voltage V G increases from 0 to 1 V. Each band energy differs with a voltage of 0.1 V. Due to a higher impurity concentration than that of the channel, a sudden peak charge density (ρ) of 6.75 × 10 26 Coul.m −3 was produced at the source and drain when V G = 0 V. With the increase in gate voltage V G = 0.5 V, the charge density (ρ) over the length of the channel decreases from 6.48 × 10 26 Coul.m −3 to 6.24 × 10 26 Coul.m −3 from the source to the midchannel and then increases when it reaches near the drain terminal, as shown in Figure 10. The charge density increases at the midchannel when gate voltage increases from 0 to 1 V with voltage difference of 0.1 V.
function of width and length, whereas the sub-band energy minima depends on [33]. Using the relationship with the carrier velocity, it is concluded that the freque electron transmission and channel length are inversely proportional with each Thus, the saturation current (ION) increases when the channel length gets reduce carriers can travel more easily through shorter gate lengths and channel lengths in parison to a longer channel, as shown previously [45]. The conduction band edge p for the GAA variant by fixing VD = 0.5 V and VG have been varied between 0 an shown in Figure 9. The device gets off at low gate voltages. When gate voltage inc the potential barrier gets lower, and the energy attained by the electrons will move from source to drain and gets lowered with an increase in drain bias. The conduction band energy decreases at the midchannel when gate voltage creases from 0 to 1 V. Each band energy differs with a voltage of 0.1 V. Due to a impurity concentration than that of the channel, a sudden peak charge density (ρ) × 10 26 Coul.m −3 was produced at the source and drain when VG = 0 V. With the incr gate voltage VG = 0.5 V, the charge density (ρ) over the length of the channel dec from 6.48 × 10 26 Coul.m −3 to 6.24 × 10 26 Coul.m −3 from the source to the midchannel an increases when it reaches near the drain terminal, as shown in Figure 10. The charg sity increases at the midchannel when gate voltage increases from 0 to 1 V with v difference of 0.1 V.  Table 3 shows the comparison modeling results of Si and GaAs Trigate the geometrical dimensions are identical for Si and GaAs NW, the accumul trons in GaAs NW is 11% more when it varies with gate voltage when co  Table 3 shows the comparison modeling results of Si and GaAs Trigate NW. Though the geometrical dimensions are identical for Si and GaAs NW, the accumulation of electrons in GaAs NW is 11% more when it varies with gate voltage when compared to Si NW. Hence, it is evident from the results that the increase in electron density of GaAs NW results in a decrease in current density, which shows that the current density depends upon the property and nature of the material and is independent of electron density. The inversion charge shifts away from the interface in the charge on the quantum modulation effect on Si and GaAs NW, which has been demonstrated to have no impact on the Subthreshold Slope (SS), as shown previously [54]. The log-scale (I D -V GS ) transfer curve with V GS at the subthreshold region has been used to calculate the Subthreshold Slope (SS), which is defined as −[d(log 10 I D )/dV G ]. The transfer characteristic curve for Si NW is shown in Figure 11. The GAA device has the highest ON current of 4.09 × 10 −5 A. Our simulation results of 15 nm Si NW are compared with GaAs NW. Figure 12 shows the transfer characteristics curve for Si and GaAs Tri-gate NW. Here, the I ON current of the GaAs Tri-gate nanowire is 10 −7 A (V S = 0 V and V D = 0.6 V), and with the silicon nanowire is 10 −13 A (V S = 0 V and V D = 0.6 V). This analysis shows that the gallium arsenide nanowire, due to its larger I ON current, has more advantages over other types of devices. The results of I ON , I OFF, and I ON /I OFF are identical values in the simulation results of the Double Gate and Omega variants, as shown clearly in Table 4 comparison results.
It was observed previously [55] that when the gate length increases to 35 nm, the I ON /I OFF ratio remains high in GAA NWs compared to all other gates. The Omega and the Double gate NWs modeling results remain the same and high when compared to the Ω -gate MoS 2 FET [56,57], which are shown in Table 4. The GAA has a smaller leakage current than any other gate and a higher conduction band energy of 8% and 37% (at 15 nm) than the Tri-gate and Pi gate. Thus, the GAA Si NW also shows a good Subthreshold Slope (SS) of 176 mV/dec, which is 39% greater than the Tri-gate NW. Therefore, the GAA device has been chosen as a better electrostatic control device.
Our proposed method has been compared with a previous study [11], where channel length (L ch = 15 nm) and oxide thickness (t ox = 1 nm) are the same. Hence, it has been observed that the increase in the gate length (L G ≥ 15 nm) and silicon dioxide material (SiO 2 ) material leads to an increase in leakage current. Thus, in our proposed method, the OFF current (I OFF ) has been reduced by various parameters, such as (1) oxide material with high dielectric constant, (2) gate length scaling, and (3) low threshold voltage. Table 5 summarizes the Si NW GAA variant with existing SiNW for an S/D doping concentration of 2 × 10 20 cm −3 . According to modeling results, the GAA NW has achieved a high I ON /I OFF ratio (1.06 × 10 9 ) when the width-to-height (W/H) ratio dimensions are equal to 1. For fixed gate and drain voltages, the small (W/H) ratio changes in the geometrical dimensions result in a low I ON /I OFF ratio, a high electron density, Subthreshold Slope (SS), and Drain Induced Barrier Lowering (DIBL). The smooth and rough surface in the channel also differs between ON and OFF currents. However, the I ON /I OFF ratios are the same in both cases, the smooth surface produces a high ON current (1 × 10 −6 A) as in Ref. [32].

Conclusions and Future Recommendations
The electrical characteristics of the NWs shielded with Lanthanum Oxide (La 2 O 3 ) material and the orientation with [001] z using the Non-Equilibrium Green Function (NEGF) method were analyzed. Using the NEGF technique, the performance of Silicon and Gallium Arsenide Nanowires with multi-gate structural arrangements, the electrical characteristics, and their parameters are computed. The comparison between all the nanowire variants was simulated. The semi-empirical tight-binding technique (sp 3 d 5 s*) was used to determine the transmission coefficient of Silicon and Gallium Arsenide nanowires for [001] orientations. The transverse dimensions of rectangular nanowires with similar energy levels have been examined, and the comparisons between Silicon and Gallium Arsenide NWs were investigated. The III-V compound semiconductor, such as GaAs NW, shows an attractive simulation in a few parameter results, such as transmission and electron density, compared to Silicon NW. Considering the issue of leakage current reduction, Silicon NWs are more suitable than Gallium Arsenide NWs.
In future work, the comparison between the same wire (Si or GaAs) with different orientations and the same orientations for different materials (Si and GaAs) should be investigated. The problems solved by Gallium Arsenide have focused on III-V compounds along with Silicon or IV-IV compounds, which could be used for applications such as energy storage, flexible electronics, and biomedical devices. Additionally, the development of new synthesis techniques may lead to the production of nanowires with novel compositions and improved properties.